How do I play Backups on my non-modded xbox360?

There is no video linked with your post.

As for your questions:
You can not play backups on an unmodified console and no, the reason you would get banned would be because the game failed a stealth check and got flagged not because it was detected to exist somewhere else.

 

Its BS, the program in the video is Imgburn.
1. Regular PC DVD drives can not read XBox discs (you need a kreon drive or an xbox drive).
2. No drive will ever make a 1:1 image of a pressed disc because there are security sectors that can't be copied in regular retail drives.
3. The XBox will not read a burned disc without the firmware being flashed.
4. Yes, you will get banned if the disc is not burned in the proper format.

 

You can only play a backup online if you've got your xbox's DVD firmware flashed with LT 3.0 or have an xkey which means you wouldn't need discs at all

 

Still works some members still use it, such as Evo85/caboose ask them

 

get it flashed or buy a xkey mate to be honest all other silly ways people reckon you can play backups without doing these is just a way of screwing it up, there's plenty of good members here on xpg that will flash your drive, just take your drive out and send it you;ll get it back withing a coulple of days all done, that's how I did mine and with ADDZ and it was a great and very fast service

 

Stanton runs a service, in the U.S.

Spoiler

http://www.xpgamesaves.com/topic/48816-us-service-one-stop-shop-for-all-your-needs-all-slims-are-exploitable